This article combines a Neural Network (NN) algorithm with the Finite Difference Time Domain (FDTD) technique to estimate the eigenfunctions in quantum devices. A NN based on the Least Mean Squares (LMS) algorithm is combined with the FDTD technique to provide a first approach to the confined states in quantum wires. The proposed technique is in good agreement with analytical results and is more efficient than FDTD combined with the Fourier Transform. This technique is used to calculate a numerical approximation to the eigenfunctions associated to quantum wire potentials. The performance and convergence of the proposed technique are also presented in this article. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2017–2022, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24562